Chapter 6
Alternative
Mortgage
Instruments
Chapter 6
Learning Objectives
Understand alternative mortgage
instruments
 Understand how the characteristics of
various AMIs solve the problems of a
fixed-rate mortgage

Interest Rate Risk

Mortgage Example:
$100,000 Fixed-Rate Mortgage @ 8% for 30
Years, Monthly Payments
PMT = $100,000 ( MC8,30) = $733.76
Interest Rate Risk

If the market rate immediately goes to 10%,
the market value of this mortgage goes to:
PV = $733.76 (PVAF10/12,360) = $83,613

Lender loses $16,387
Interest Rate Risk

If the lender can adjust the contract
rate to the market rate (10%), the
payment increases and the market
value of the loan stays constant:
Pmt = $100,000 (MC10,30) = $877.57
PV = $877.57 (PVAF10/12,360) =
$100,000
Alternative Mortgage
Instruments
Adjustable-Rate Mortgage (ARM)
 Graduated-Payment Mortgage (GPM)
 Price-Level Adjusted Mortgage (PLAM)
 Shared Appreciation Mortgage (SAM)
 Reverse Annuity Mortgage (RAM)
 Pledged-Account Mortgage or Flexible
Loan Insurance Program (FLIP)

Adjustable-Rate Mortgage
(ARM)




Designed to solve interest rate risk problem
Allows the lender to adjust the contract
interest rate periodically to reflect changes in
market interest rates. This change in the rate
is generally reflected by a change in the
monthly payment
Provisions to limit rate changes
Initial rate is generally less than FRM rate
ARM Variables
Index
 Margin
 Adjustment Period
 Interest Rate Caps

– Periodic
– Lifetime
Convertibility
 Negative Amortization
 Teaser Rate

Determining The Contract
Rate
Fully Indexed:
Contract Rate (i) = Index + Margin
 In general, the contract rate in time n is
the lower of

in= Index + Margin
or
in = in-1 + Cap
ARM Example
Loan Amount = $100,000
 Index = 1-Year TB Yield
 One Year Adjustable
 Margin = 2.50
 Term = 30 years
 2/6 Interest Rate Caps
 Monthly Payments
 Teaser Rate = 5%

ARM Payment In Year 1

Index0 = 5%

Pmt1 = $100,000 (MC5,30) = $536.82
ARM Payment In Year 2

BalanceEOY1= 536.82 (PVAF5/12,348) = $98,525
Interest Rate for Year 2
IndexEOY1 = 6%
i = 6 + 2.50 = 8.5%
or
i = 5 + 2 = 7%
 Payment2 = $98,525 (MC7,29) = $662.21

ARM Payment In Year 3
BalanceEOY2 = $662.21 (PVAF7/12,336) =
$97,440
 Interest Rate for Year 3
 IndexEOY2 = 6.5%
i = 6.5 + 2.5 = 9%
or
i = 7 + 2 = 9%
 Pmt3 = 97,440 (MC9,28) = $795.41

Simplifying Assumption

Suppose Index3-30 = 6.5%

This means that i3-30 = 9% since the contract
rate in year 3 is fully indexed

Thus Pmt3-30 = $795.41

BalEOY3 = $96,632
ARM Effective Cost for a
Three-Year Holding Period

$100,000 = 536.82 (PVAFi/12,12)
+ 662.21 (PVAFi/12,12) (PVFi/12,12)
+ 795.41 (PVAFi/12,12) (PVFi/12,24)
+ 96,632 (PVFi/12,36)
i = 6.89%
ARM Annual Percentage
Rate (APR)

$100,000 = 536.82 (PVAFi/12,12)
+662.21 (PVAFi/12,12) (PVFi/12,12)
+795.41 (PVAFi/12,336) (PVFi/12,24)
i = 8.40%
Interest-Only ARM




Payment in the initial period is interest-only
with no repayment of principal
After the initial period the loan becomes fully
amortizing
Loan is designed to fully amortize over its
stated term
A 3/1 Interest-Only ARM is interest-only for
the first three years and then becomes a fully
amortizing one-year ARM
Interest-Only ARM

Suppose you take a 3/1 interest-only
ARM for $120,000, monthly payments,
30-year term. The initial contract rate is
4.00% and the contract rate for year 4
is 6.00%. The lender charges two
discount points.
Interest-Only ARM
What is the monthly payment for the
interest-only period?
$120,000 (.04/12) = $400.00
Interest-Only ARM
What is the effective cost of the loan if
it is repaid at the EOY3?
120,000 – 2,400 = 400 (PVAFi/12,36)
+ 120,000 (PVFi/12,36)
i = 4.72%
Interest-Only ARM
What is the payment for year 4?
Pmt = 120,000 (MC6,27)
Pmt = $748.78
Interest-Only ARM
What is the balance of the loan at the
EOY 4 of the 30-year term?
BalEOY4 = 748.78 (PVAF6/12,312)
= $118,165
Interest-Only ARM
If the loan is repaid at the EOY4, what
is the effective cost?
120,000 – 2,400 = 400 (PVAFi/12,36)
+ 748.78 (PVAFi/12,12)
+ 118,165 (PVFi/12,48)
i = 5.0145%
Option ARM




Gives the borrower the flexibility of several
payment options each month
Includes a “minimum” payment, an interestonly payment, and a fully Amortizing payment
Usually has a low introductory contract rate
Minimum payment results in negative
amortization
Option ARM




Minimum payment can result in “payment
shock” when payment increases sharply
Loan must be recast to fully amortizing every
five or ten years
Negative amortization maximum of 125% of
original loan balance
Loan payment increases to fully amortizing
level
Alt-A Loan




Alternative Documentation Loan or “No Doc”
Loan
Borrower may not provide income verification
or documentation of assets
Loan approval based primarily on credit score
In the mid-2000s, loans were popular with
non owner-occupied housing investors
Flexible Payment ARM




Very low initial payment, expected to rise
over time
“Payment shock” with dramatic increase in
payment
Appeal is the very low initial payment
designed to help offset affordability problem
Contract rate adjusts monthly with maybe no
limits on size of interest rate changes
Graduated-Payment
Mortgage (GPM)


Tilt effect is when current payments reflect
future expected inflation. Current FRM
payments reflect future expected inflation
rates. Mortgage payment becomes a greater
portion of the borrower’s income and may
become burdensome
GPM is designed to offset the tilt effect by
lowering the payments on an FRM in the
early periods and graduating them up over
time
Graduated-Payment
Mortgage (GPM)





After several years the payments level off for
the remainder of the term
GPMs generally experience negative
amortization in the early years
Historically, FHA has had popular GPM
programs
Eliminating tilt effect allows borrowers to
qualify for more funds
Biggest problem is negative amortization and
effect on loan-to-value ratio
Price-Level Adjusted
Mortgage (PLAM)




Solves tilt problem and interest rate risk
problem by separating the return to the
lender into two parts: the real rate of return
and the inflation rate
The contract rate is the real rate
The loan balance is adjusted to reflect
changes in inflation on an ex-post basis
Lower contract rate versus negative
amortization
PLAM Example
Suppose you borrow $100,000 for 30 years,
monthly payments. The current real rate is
6% with annual payment adjustments

EOY
1
2
3
4-30

Inflation
4%
-3%
2%
0%
PLAM Payment in Year 1
Pmt = $100,000 ( MC6,30) = $599.55
PLAM Payment in Year 2
BalEOY1 = $98,772 (1.04) = $102,723
Pmt2 = $102,723 (MC6,29) = $623.53
PLAM Payment in Year 3
BalEOY2 = $101,367 (.97) = $98,326
Pmt3 = $98,326 (MC6,28) = $604.83
PLAM Payment in Year 4
BalEOY3 = $96,930 (1.02) = $98,868
Pmt4 = $98,868 (MC6,27) = $616.92
PLAM Payment in Years 5-30
BalEOY4 = $97,356 (1.00) = $97,356
Pmt5-30 = $97,356 (MC6,26) = $616.92
PLAM Effective Cost If Repaid
at EOY3

$100,000 = 599.55 (PVAFi/12,12)
+ 623.53 (PVAFi/12,12) (PVFi/12,12)
+ 604.83 (PVAFi/12,12) (PVFi/12,24)
+ 98,868 (PVFi/12,36)
i = 6.97%
PLAM Effective Cost If Held
To Maturity (APR)

$100,000 = 599.55 (PVAFi/12,12)
+ 623.53 (PVAFi/12,12) (PVFi/12,12)
+ 604.83 (PVAFi/12,12) (PVFi/12,24)
+ 616.92 (PVAFi/12,324) (PVFi/12,36)
i = 6.24%
Problems with PLAM
Payments increase at a faster rate than
income
 Mortgage balance increases at a faster
rate than price appreciation
 Adjustment to mortgage balance is not
tax deductible for borrower
 Adjustment to mortgage balance is
interest to lender and is taxed
immediately though not received

Shared Appreciation
Mortgage (SAM)
Low initial contract rate with inflation
premium collected later in a lump sum
based on house price appreciation
 Reduction in contract rate is related to
share of appreciation
 Amount of appreciation is determined
when the house is sold or by appraisal
on a predetermined future date

Reverse Mortgage

Typical Mortgage - Borrower receives a
lump sum up front and repays in a
series of payments

Reverse Mortgage - Borrower receives a
series of payments and repays in a
lump sum at some future time
Reverse Mortgage

Typical Mortgage - “ Falling Debt, Rising
Equity”

Reverse Mortgage - “ Rising Debt,
Falling Equity”
Reverse Mortgage
Loan advances are not taxable
 Designed for senior homeowners for
little or no mortgage debt
 Social Security benefits are generally
not affected
 Interest is deductible when paid

Reverse Mortgage

Reverse Mortgage Can Be:
– A cash advance
– A line of credit
– A monthly annuity
– Some combination of above
Reverse Mortgage Example
Borrow $200,000 at 9% for 5 years, Annual Pmts.
Yr
1
2
3
4
5
Beg. Bal. Pmt
Interest End Bal.
0
30659
2759
33418
33418
30659
5767
69844
69844
30659
9045 109548
109548
30659
12619 152826
152826
30659
16514 199999
Pledged-Account Mortgage




Also called the Flexible Loan Insurance
Program (FLIP)
Combines a deposit with the lender with a
fixed-rate loan to form a graduated-payment
structure
Deposit is pledged as collateral with the
house
May result in lower payments for the
borrower and thus greater affordability
Mortgage Refinancing



Replaces an existing mortgage with a new
mortgage without a property transaction
Borrowers will most often refinance when
market rates are low
The refinancing decision compares the
present value of the benefits (payment
savings) to the present value of the costs
(prepayment penalty on existing loan and
financing costs on new loan)
Mortgage Refinancing

Factors that are known to the borrower
or can be calculated from the existing
mortgage contract:
– Current
– Current
– Current
– Current
contract rate
payment
remaining term
outstanding balance
Mortgage Refinancing

Assumptions that must be made by the
borrower:
– What will be the amount of the new loan?



Payoff of the existing loan?
Payoff of the existing loan plus financing costs
of the new loan?
Payoff of the existing loan plus financing costs
of the new loan plus equity to be taken out?
Mortgage Refinancing

Assumptions that must be made by the
borrower:
– What will be the term of the new loan?



Equal to the remaining term of the existing
loan?
Longer than the remaining term of the existing
loan?
Shorter than the remaining term of the existing
loan?
Mortgage Refinancing

Assumptions that must be made by the
borrower:
– What will be the holding period of the
financing?


Equal to the term (maturity) of the mortgage?
Shorter than the term (maturity) of the
mortgage?